We emphasize that the asymptotic convergence rate requires Assumptions REF , REF (REF , ), REF , REF , while the asymptotic normality and Berry-Esseen bound require us to impose Assumption REF  and strengthen (REF ) to (), although the asymptotic rate is also improved under stronger conditions.
To adopt the covariance estimator \(\Xi _t\) , () need to be further strengthen to (). However, even for the most stringent conditions () and (), they are quite common in the literature [1]}, and they enable wide applications including constrained least squares and constrained logistic regression.
